Sitagliptin in Recurrent/Progressive Grade 4 Glioma

Inclusion Criteria: Phase 1b * Subjects must have histologically or cytologically confirmed WHO grade 4 glioma for which disease recurrence/progression is diagnosed by the treating physician. * Subjects must not have received sitagliptin or bevacizumab for this disease. * Age \>18 years * Performance status: ECOG performance status 0-2 * Subjects must have adequate organ function and laboratory parameters within 21 days of study entry as defined below: 1. Hemoglobin ≥ 9 g/dl 2. Absolute neutrophil count ≥ 1,500/mcL 3. Platelet count ≥ 100,000/mcL 4. Total bilirubin \< 1.5 x institutional upper limit of normal (ULN) 5. AST (SGOT) ≤ 3 X institutional ULN 6. ALT (SGPT) ≤ 3 X institutional ULN 7. Calculated creatinine clearance \> 50 mL/min 8. Urine protein screened by urine analysis for urine protein creatinine (UPC) ratio. For UPC ratio \> 0.5, 24-hour urine protein must be obtained and must be \< 1000 mg. 9. Patients on full-dose anticoagulants (e.g., warfarin or LMW heparin) must meet both of the following criteria: * No active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices) * In-range INR (between 2 and 3) on a stable dose of oral anticoagulant or on a stable dose of low molecular weight heparin * Subjects must have the ability to understand and the willingness to sign a written informed consent document. * Women of childbearing potential must have a negative pregnancy test within 7 days prior to treatment start. Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and through 30 days after the last dose of study drug. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and through 30 days after the last dose of study drug. * Subjects must be able to swallow whole tablets. * Participants must have controlled blood pressure, defined as systolic blood pressure ≤ 160 mg Hg or diastolic pressure ≤ 100 mg Hg, with or without antihypertensive therapy * Electrocardiogram without evidence of acute cardiac ischemia within 14 days prior study registration * Subjects must have the following minimum intervals from prior treatments: * surgery - 4 weeks * nitrosoureas - 6 weeks * cytotoxic chemotherapy - standard intervals depending on the most recent regimen. i.e., for temozolomide 5 of 28, 23 days after most recent temozolomide; for temozolomide 21 of 28 days, 7 days after most recent dose; etoposide 14 of 21 days, 7 days after last dose. * For drugs not listed, the research nurse, treating investigator, and principal investigator will determine the appropriate interval. * Investigational therapy or non-cytotoxic therapy - 2 weeks * For bevacizumab - 4 weeks from the expected date of protocol surgery * Subject is not deemed as a surgical candidate. Pilot Phase * Subjects must have histologically or cytologically confirmed WHO grade 4 glioma for which disease recurrence/progression is diagnosed by the treating physician. * Subjects must not have received sitagliptin or bevacizumab for this disease. * Age \>18 years * Performance status: ECOG performance status 0-2 * Subjects must have adequate organ function and laboratory parameters within 21 days of study entry as defined below: 1. Hemoglobin ≥ 9 g/dl 2. Absolute neutrophil count ≥ 1,500/mcL 3. Platelet count ≥ 100,000/mcL 4. Total bilirubin \< 1.5 x institutional upper limit of normal (ULN) 5. AST (SGOT) ≤ 3 X institutional ULN 6. ALT (SGPT) ≤ 3 X institutional ULN 7. Calculated creatinine clearance \> 50 mL/min 8. Urine protein screened by urine analysis for urine protein creatinine (UPC) ratio. For UPC ratio \> 0.5, 24-hour urine protein must be obtained and must be \< 1000 mg. 9. Patients on full-dose anticoagulants (e.g., warfarin or LMW heparin) must meet both of the following criteria: * No active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices) * In-range INR (between 2 and 3) on a stable dose of oral anticoagulant or on a stable dose of low molecular weight heparin * Subjects must have the ability to understand and the willingness to sign a written informed consent document. * Women of childbearing potential must have a negative pregnancy test within 7 days of treatment start. Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and through 30 days after the last dose of study drug. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and through 30 days after the last dose of study drug. * Subjects must be able to swallow whole tablets. * Subjects must have controlled blood pressure, defined as systolic blood pressure ≤ 160 mg Hg or diastolic pressure ≤ 100 mg Hg, with or without antihypertensive therapy * Electrocardiogram without evidence of acute cardiac ischemia within 14 days prior to treatment start * Subjects must have the following minimum intervals from prior treatments: * surgery - 4 weeks * nitrosoureas - 6 weeks * cytotoxic chemotherapy - standard intervals depending on the most recent regimen. i.e., for temozolomide 5 of 28, 23 days after most recent temozolomide; for temozolomide 21 of 28 days, 7 days after most recent dose; etoposide 14 of 21 days, 7 days after last dose. * For drugs not listed, the research nurse, treating investigator, and principal investigator will determine the appropriate interval. * Investigational therapy or non-cytotoxic therapy - 2 weeks * For bevacizumab - 4 weeks from the expected date of protocol surgery * Subject is deemed as a surgical candidate. Exclusion Criteria (for phase 1b and pilot phase) The presence of any of the following will exclude a subject from study enrollment: * Prior treatment toxicities not resolved to ≤ Grade 1 according to NCI CTCAE Version 5.0 except for alopecia and neuropathy. * Subjects receiving any other investigational agents. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to sitagliptin, bevacizumab, or other chemotherapy agents. * Subjects with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Known HIV-positive subjects on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with sitagliptin and/or bevacizumab. In addition, these subjects are at increased risk of lethal infections when treated with marrow suppressive therapy. * Other malignancy within the past 2 years with the exception of a) adequately treated basal cell carcinoma, squamous cell skin cancer, or thyroid cancer; b) carcinoma in situ of the cervix or vulva; c) prostate cancer of Gleason Score 6 or less with stable prostate-specific antigen levels; or d) cancer considered cured by surgical resection or unlikely to impact survival during the duration of the study, such as localized transitional cell carcinoma of the bladder, or benign tumors of the adrenal or pancreas. * Significant chronic gastrointestinal disorder with diarrhea as a major symptom (e.g., Crohn's disease, malabsorption, or Grade ≥2 (National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events Version 5.0 \[CTCAE v.5.0\] diarrhea of any etiology at screening). * Known active infection with hepatitis B or hepatitis C virus. * Pregnant or breastfeeding. * Subjects who receive insulin or sulfonylurea for diabetes mellitus. * Subjects with history of type 1 diabetes, uncontrolled type 2 diabetes, hypoglycemia requiring medical intervention, or those who are deemed not suitable to receive sitagliptin at the discretion of the investigators. * Unable or unwilling to swallow tablets. * Evidence of significant medical illness, abnormal laboratory finding, or psychiatric illness/social situations that would, in the Investigator's judgment, make the patient inappropriate for this study. * Arterial ischemic event (e.g., unstable angina, myocardial infarction, stroke) within 6 months of study entry. * Subjects with history of hematologic bleeding disorder.